Part II: Kinematics, the fundamentals

This section will provide an overview of the fundamental concepts in kinematics. This will include the following topics:

1. What is Kinematics?

2. Kinematics within mechanics

3. Key definitions

4. Motion and kinematic pairs

5. Transmission of motion

6. Mobility

7. Review of some general classes of Mechanisms

1: What is Kinematics?

“Kinematics is the study of ______

Kinetics is the study of ______on systems in motion:

Underlying Assumptions in Kinematics:

1)Rigid bodies

2)Ignore forces (applied, friction, etc)

3)Bodies are connected by Joints – Kinematic pairs

4)The nature of connection b/n kinematic pairs is maintained

This is kinematics,

and this is kinematics,

This is NOT kinematics,

Why Kinematics? Why Machines?

Create / harness energy (non-human energy)

Manufacturing, agriculture

Assistive / serve humans

What is the future of kinematics and machinery?

Miniature, micro and perhaps even nano-scale machines (motion at a micro or molecular level)

Medical, rehabilitative, prosthetic

Self-replication of machinery, machines design machines

Machines become more biological in nature (compliant, biological muscles, intelligent).

2. Kinematics within Mechanics

Kinematics and the theory behind machines have a long history. Kinematics has evolved to become a unique component within Mechanics as demonstrated in this figure

3. A few key definitions:

Kinematics

Dynamics

Mechanism

Machine

Degrees of freedom

Constraint

Mobility

4. Motion (of a rigid body): displacement of a rigid body w.r.t. a fixed frame or reference frame (for dynamics, needs to be an IRF).

Translation:

Rotation:

Planar:

Spatial:

Kinematic Pairs: Two members (links) are jointed through a connection (joint) that defines the relative motion b/n the two.

More about joints:

Classically classified into a couple classes: Higher pair (point contact) and Lower pair (line contact).

Various types of joints:

Revolute:

Prismatic (slider)

Cam or gear

Rolling contact

Spring

Others?

5.Transmission of Motion: The motion of a mechanism is defined by its constraints (kinematic). The following example shows one of the most general cases of motion between two bodies and demonstrates some key elements in understanding the behavior of motion. Consider two general kinematic bodies (rigid bodies, known geometric properties) in contact at point P. Each body rotates about a fixed point, O2 and O3.

Notes:

1)A common Normal and tangent (N, t) exist and are defined by the 2 surfaces

2)“Condition of contact”: no relative motion can occur along the common normal

3)All sliding takes place along the common tangent

4)The result of these rules (plus some geometric construction):

5)Requirement for constant velocity:

6)Requirement for no sliding:

6. Mobility Analysis:

Mobility is defined as the number of dof. Mobility is calculated as the total number of possible degrees of freedom, minus the number of constraints. The following diagrams will demonstrate the process:

ItemDiagramDOF

One body

Two Bodies

Two bodies connected

by a revolute

Ground (it is a body)

Writing these rules as equations yields:

Which is known as Grubler’s or the Kutzbach equation.

Note: when M = 0 Structure, statically determinant

M < 0  Indeterminant structure

M > 0 Mechanism with M dof

Simple Mobility Examples:

Mobility Examples (list 4-6 examples for in-class practice 3 line drawings, 3 photos)


EXTRA STUFF: Mobility as a synthesis tool:

Sketch a 1 dof mechanism having exactly 5 links:

EXTRA STUFF: 7. Review of some general classes of Mechanisms

(More about each of these general mechanism types to follow later in the course)

1. Linkages:

The most famous types of linkages include the 4-bar, slider crank. Followed by five-bars and six bars.

The four-bar:

Slider Crank:

2. Cam mechanisms:

3. Gear Mechanisms

4. Chain and Sprocket / Belt and Pulley

5. Intermittent motion devices: Geneva Wheel

Part II -1

ME 3610 Course Notes - Outline